Parameter recovery in two-component contamination mixtures: the $L^2$ strategy

Sébastien Gadat (1, 2) , Jonas Kahn (3) , Clément Marteau (4) , Cathy Maugis-Rabusseau (3)

1 TSE-R - Toulouse School of Economics
2 UT Capitole - Université Toulouse Capitole
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 ICJ - Institut Camille Jordan

In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, f = (1 − λ)φ + λ φ(. − µ), where the shape φ is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters (λ , µ) ∈ (0, 1) × R^d. In particular, we prove that the classical parametric rate 1/ √ n cannot be reached when at least one of these parameters is allowed to tend to 0 with n.

Mots clés: $L^2$ contrast; parameter estimation; rate of convergence; two-component contamination mixture model

Domaines: Statistiques [math.ST]

Sébastien Gadat, Jonas Kahn, Clément Marteau, Cathy Maugis-Rabusseau. Parameter recovery in two-component contamination mixtures: the $L^2$ strategy. 2018. ⟨hal-01713035v1⟩